A Spectral Factorization Approach to Pseudo-QMF Design

A new approach to the design of M-channel pseudoquadrature-mirror-filter (QMF) banks is presented. In this approach, the prototype filter is obtained as a spectral factor of a 2Mth band filter. This completely eliminates the need for optimization whereas in conventional pseudo-QMF designs, the main computational effort is in optimization of the prototype. As in the conventional approach, the aliasing cancellation (AC) constraint ensures that all the significant aliasing terms are canceled. The overall transfer function T(z) of the analysis/synthesis system has a linear phase and an approximately “flat” magnitude response in the frequency region ε ≤ ω ≤ (π - ε), where ε depends on the transition bandwidth of the prototype and 0 < ε < (π/2M). Three design examples are included

An Iterative Design with Variable Step Prototype Filter for Cosine Modulated Filter Bank

A systematic and self controlled prototype filter design approach for multichannel Cosine Modulated Near Perfect Reconstruction (NPR) filter bank is proposed in this paper. The primary goal is to design a prototype filter with enhanced performance i.e., minimum amplitude distortion and aliasing error. This algorithm approximates 3dB cutoff frequency very close to π/2M. This is achieved by selecting suitable step size which is a function of transition width. If the selection of step size is too fine, the objective function oscillates. Whereas, if step size is coarse, 3dB cutoff frequency will not be close to π/2M. This will degrade the overall performance of the prototype filter. Thus by choosing the step size as a function of transition width and varying the step size from coarser to finer level, the minimum amplitude distortion and aliasing error can be definitely achieved. The proposed filter is designed using two input parameters: number of subbands M and attenuation A and all other system parameters are derived from it to avoid heuristic inputs. Simulation results indicate better performance with reference to algorithms existing in literature. In addition, the design approach is systematic and self controlled

Design of low-delay nonuniform pseudo QMF banks

Journal ArticleABSTRACT This paper presents a method for designing low-delay nonuniform pseudo QMF banks. The method is motivated by the work of Li, Nguyen and Tantaratana, in which the nonuniform filter bank is realized by combining an appropriate number of adjacent subbands of a uniform pseudo QMF filter bank. In prior work, the prototype filter of the uniform pseudo QMF is constrained to have linear phase and the overall delay associated with the filter bank was often unacceptably large for filter banks with a large number of subbands. By relaxing the linear phase constraints, this paper proposes a pseudo QMF filter bank design technique that significantly reduces the delay. An example that experimentally verifies the capabilities of the design technique is presented

On the design of nearly-PR and PR FIR cosine modulated filter banks having approximate cosine-rolloff transition band

This paper proposes an efficient method for designing nearly perfect reconstruction (NPR) and perfect reconstruction (PR) cosine modulated filter banks (CMFBs) with prototype filters having an approximate cosine-rolloff (CR) transition band. It is shown that the flatness condition required for an NPR CMFB can be automatically satisfied by using a prototype filter with a CR transition band. The design problem is then formulated as a convex minimax optimization problem, and it can be solved by second-order cone programming (SOCP). By using the NPR CMFB so obtained as an initial guess to nonlinear optimizers such as Fmincon in Matlab, high-quality PR CMFBs can be obtained. The advantages of the proposed method are that it does not require a user-supplied initial guess of the prototype filter and bumps in the passband of the analysis filters can be effectively suppressed. © 2008 IEEE.published_or_final_versio

Design of near-perfect-reconstructed transmultiplexer using different modulation techniques: A comparative study

AbstractIn this paper, an efficient iterative method for design of near-perfect reconstructed transmultiplexer (NPR TMUX) is proposed for the prescribed roll-off factor (RF) and stop band attenuation (As). In this method, windowing technique has been used for the design of prototype filter, and different modulation techniques have been exploited for designing multi-channel transmultiplexer (TMUX). In this method, inter-channel interference (ICI) is iteratively minimized so that it approximately reduces to ideal value zero. Design example is given to illustrate the superiority of the proposed method over earlier reported work. A comparative study of the performance of different modulation techniques for designing TMUX is also presented

Optimum Design of Linear Phase Paraunitary Filter Bank & its Applications in Signal Processing

Filter Banks plays crucial role in signal processing and image processing as subband processing gives dominant results in time critical applications. In formal years, various Para unitary Linear Phase Filter Banks are proposed by following conventional and computational complex factorization and lattice approaches consisting of complex nonlinear optimization problems. One of the recent methods to design Filter Bank having properties of Linear Phase and Paraunitary is via Singular value decomposition technique which leads to optimum results compared to existing methods as most of the time it deals with matrix operations. In this paper, design benchmark is evaluated as two dominant optimization queries and reasonable key of each optimization query is solved by performing Singular Value Decomposition. Proposed Paper discusses linear phase condition of filter banks satisfying mirror image symmetry at analysis side and perfect reconstruction property at synthesis side. Singular Value Decomposition approach leads to fast and efficient simulation results compared to existing filter banks designs. Proposed method of filter bank design deals with any arbitrary channels and every length of the filters

Low-delay nonuniform pseudo-QMF banks with application to speech enhancement

Journal ArticleAbstract-This paper presents a method for designing low-delay nonuniform pseudo quadrature mirror filter (QMF) banks. This method is motivated by the work of Li, Nguyen, and Tantaratana, in which the nonuniform filter bank is realized by combining an appropriate number of adjacent sub-bands of a uniform pseudo-QMF bank. In prior work, the prototype filter of the uniform pseudo-QMF bank was constrained to have linear phase and the overall delay associated with the filter bank was often unacceptably large for filter banks with a large number of sub-bands. This paper proposes a pseudo-QMF filter bank design technique that significantly reduces the delay by relaxing the linear phase constraints. An example in which an oversampled critical-band nonuniform filter bank is designed and applied to a two-state modeling speech enhancement system is presented in this paper. Comparison of the performance of this system to competing methods employing tree-structured, linear phase multiresolution analysis indicates that the approach described in this paper strikes a good balance between system performance and low delay

On the theory and design of a class of PR uniform and recombination nonuniform causal-Stable IIR cosine modulated filter banks

This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in z M, where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly. © 2008 IEEE.published_or_final_versio